Initial Research Possessed: the ride features zero-gravity and cobra rolls and corkscrews. A cobra roll takes the rider upside down twice, and a corkscrew resembles a typical loop that has been stretched out. In a corkscrew, riders are angled at 90 degrees horizontally from the incoming track. Talon: the ride is floorless and uses a zero-gravity roll and an Immelman loop. The former places the center of gravity on the rider's heart to make him feel weightless, and the latter is an inverted loop where the rider's head is perpendicular to the track below him. http://en.wikipedia.org/wiki/Immelmann_loop#Immelmann_loop
What Do You See? Someone is being pushed in a wheely chair at various velocities and accelerations like they are on a roller coaster.
What Do You Think? The parts that have the greatest amount of acceleration and turns creates the loudest screams, like the loops.
Physics Talk Scaler: a quantity that has magnitude (size/amount), but no direction Displacement: the difference in position between a final position; it depends only on the endpoints, not the path; displacement is a vector quality, it has magnitude (size) and direction Vector: a quantity that has both magnitude (size/amount) and direction Speed: distance traveled divided by the time elapsed; speed is a scaler quantity, it has no direction Velocity: displacement divided by the time elapsed; velocity is a vector quantity, it has magnitude and direction Acceleration: The change in velocity divided by the time elapsed; acceleration is a vector quantity, it has magnitude and direction
Checking Up 1) Displacement is the difference in position between a final position, whereas distance is the total difference between the start and the final positions. 2) 0 km because you wound up where you started 3) Speed is distance divided by time whereas velocity is displacement divided by time. 4) Total change in velocity over total change in distance = acceleration
What Do You Think Now? The downward hills cause the most amount of acceleration, therefore producing the loudest scream. During the investigation, I felt the most jolted when experiencing quick accelerations.
Physics To Go 1) 2) The acceleration around curves and drops creates the largest thrills.
3A) La Paz in Bolivia has the greatest speed; it travels the greatest distance 3B) v = d/t v = 40,000 / 24 v = 1666 2/3 m/s 3C) It has a high speed but because of its consistency it does not feel like you are going fast
8) a = v/t a = vf - vi / t a = 25-0 / 10 a = 2.5 m/s^2
10A) To make it more enjoyable for younger kids, I would alter the angle to make it less extreme for the kids. Anything to steep or scary would be too scary. 10B)
Section 2
What Do You See? The people around the bend are sleeping, while the people going down the hill are screaming.
What Do You Think? The steel roller coaster has the biggest thrill because of its steeper angle in comparison to the wooden roller coaster's 60 degree angle.
Physics Talk GPE: The energy a body possesses as a result of its position in a gravitational field KE: The energy an object possesses because of its speed Joule: The unit for energy Mechanical Energy: The sum of GPE + KE Bar Chart:
Checking Up 1) When lengthening the incline, the ball will have a faster velocity at the bottom of the ramp. 2) Because GPE = mgh, any increase in a variable will increase the amount of energy in the object's potential energy. 3) The same goes for kinetic energy as it does for GPE. However, velocity is the only variable that is squared, so it carries more weight than the rest. 4) The cart starts with GPE and that turns into KE when it is released down the ramp. Because mechanical energy is GPE + KE, then the energy remains the same. 5) KE + GPE(bottom) = KE + GPE(top) 3/4(40,000)(Kinetic Energy) + 1/4(40,000)(GPE) = 0 + 40,000 KE = 30,000 J
What Do You Think Now? When the carts start at the same height, their velocity and final magnitude are the same. Regardless of the incline, the carts will have the same velocity when traveling the same distance; however, the shorter track is going to be the one with the cart to finish first. This proves that the bigger the acceleration, the bigger the thrill.
Physics To Go 1) The speeds are both the same because the distance does not change. However, graph B would be faster if friction played a role.
3)
60,000
0
60,000
0
60,000
60,000
30,000
30,000
60,000
15,000
45,000
60,000
5)
300(10)(25) = 75000
0
75,000
0
75,000
75,000
37,500
37,500
75,000
300(10)(5) = 15,000
60,000
75,000
4 + 6)
8) KE and GPE both have mass in their equations, so when set equal to one another the masses cancel out; any system that uses gravity doesn't need mass to be solved.
9A) Point B showcases where the energy has changed from the highest GPE to the highest KE. The acceleration is maximized here, but as it goes back up the hill, the object will lose its KE but gain GPE proportionally. 9B) Ignoring friction, points B and G are the same height off of the ground and therefore have the same GPE and KE. 9C) Point D is where the object moves the fastest because of its low GPE and high KE.
Section 3
What Do You See? Students are playing with spring toys and measuring its vertical distance.
What Do You Think? Roller coaster carts usually need to go up a hill, so they either get pulled or move up a track. Carts full of people need more energy to lift it because the mass is now heavier.
Physics Talk Spring Potential Energy: the energy stored in a spring due to its compression or stretch
Checking Up 1) That energy is then translated into kinetic energy once it is popped upward. 2) Energy cannot be created or destroyed, so the 2 J of SPE is transferred as 2 J of KE 3) Once again, energy cannot be created or destroyed. That energy is now 2 J of GPE 4) SPE = 1/2(k)(x^2)
Physics To Go 5) The cart moves up a hill and at its peak it has a maximum GPE. Once that energy is transformed into KE, it then can move up and down hills. However, the maximum energy has been reached, so the next hill cannot exceed the previous. 6) The cart has a certain amount of kinetic energy at the start of the roller coaster. To go up and down hills, the cart needs to maintain a certain energy to do so; when the cart does not have the amount, it slows down until it finally will come to a stop. 7) GPE = mgh = 300(9.8)(15) = 44,100 J
8A) KE = 1/2m(v^2) = 1/2(400)(15^2) = 45,000 J 8B) The GPE will be 45,000 J of energy if the kinetic energy is 0 8C) 45000 = 400(9.8)h h = 11.48 m
9) The GPE is maximized at its highest point, so when rising it's GPE is increasing and when it falls its decreasing. 10) All three people will have the same GPE in the end, but whoever walks on route A will gain the most GPE the fastest.
11A) GPE = KE 0.02(9.8)(0.4) = 1/2(0.02)(2.7^2) 0.0784 = 0.0729 The values are very similar.
11C) The height would reach 1/3 of its original height.
12A) GPE = EPE mgh = 1/2k(x^2) 300(9.8)(18) = 1/2(4)(x^2) 52920 = 2x^2 26460 = x^2 x = 162.67 m
12B) GPE = EPE mgh = 1/2k(x^2) 400(9.8)(18) = 1/2(4)(x^2) 70560 = 2x^2 35280 = x^2 x = 187.83 m
13) EPE = KE 1/2k(x^2) = KE 1/2(40)(.3^2) = KE KE = 1.8 J
What Do Yu Think Now? With most roller coasters, a chain drags the carts up a hill to reach a certain height in order to fulfill the needed amount of energy to ride the track. The amount of energy needed to lift the cart fully depends on the mass of the cart with the maximum weight of all of the passengers. This is why roller coasters have weight limits, to ensure safety when reaching maximum GPE.
Section 4
What Do You See? The astronauts on the moon are on a roller coaster, but do not seem to be having fun. However, Jupiter's roller coaster has them screaming in delight.
What Do You Think? Gravity points to the center of the Earth, regardless of what direction you are facing. Liquids that drain in Australia turn the opposite way than in America due to the change in gravity.
Physics Talk Gravitational Field: the gravitational influence in the space around a massive object Inverse-square Relationship: the relationship between the magnitude of a gravitational force and the distance from the mass. This also describes how electrostatic forces depend on the distance from an electrical charge Newton's Law of Universal Gravitation: all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bodies increases. Gravity: the force of attraction between the two bodies due to their masses
Checking Up 1) Gravity pulls towards the center of the earth. 2) Gravity is stronger where the lines are closest together whereas the further away from the center, the weaker the gravity. 3) The gravity is then cubed. 4) The moon and its orbit is held together by the same gravity 5) The shape of the orbit around the sun is elliptical.
Physics Plus 1) a = (v^2)(r) 2) v = d/t (2pi)(3.84 x 10^8) / 2440800 v = 998.51 m/s 3) a = v^2 / r a = 998.51^2 / (3.84 x 10^8) a = 0.0025 m/s^2
Physics To Go 1) 1/25
2A) 1/4 of the force 2B) 1/9 of the force 2C) 1/16 force.
3) Every mass has gravitational force, so the GPE will always be present. This is a secure fact, so there is no reason to distrust it.
4) Both values of GPE and KE (when set equal to one another) are very similar. The only slight difference is that the point at the top will have a miniscule amount less than the cart at the bottom because of the difference in height. The closer to the earth, the more gravity it will have.
5A) The water sits on the Earth. 5B&C) More water on the side facing the moon because the water is attracted to the moon's pull
6A&B) Water's polarity has a gravitational pull, and the fish also has GPE. This keeps the water and the fish grounded.
7A) 1/4 of the force. 7B) 1/9 of the force. 7C) 1/16 of the force. 7D) 4x the force
8A) Doubles 8B) Triples 8C) Quadruples 8D) Half
9A) Quadruples 9B) 9x the force 9C) 16x the force 9D) 1/4 of the force
10A) Doubles 10B) 9x the force 10C) 6x the force
What Do You Think Now? Attraction between two masses accounts for gravity's direction. Because everything is pulled towards the center of the Earth, people do not feel upside down regardless of their geographical location. Gravity acts on all masses, so the ground is attracted to the center of the earth, and we are attracted to the ground.
Section 5
What Do You See?
The same piece of meat is being weighed by 2 different scales - one at a deli and one at a lab.
What Do You Think?
A scale that measures an elephant would not be able to make sense of the small mass of the canary and vice versa. A scale works by a mass stepping on it and stretching the coil. The distance is measured and recorded for the person to see their weight, also in combination with gravity.
Physics Talk Hooke's Law: Fs = -kx (F = force of spring in N; k = spring constant in N/m; x = stretch distance in m)
Force is opposite distance
Slope is the spring constant
Checking Up 1) The spring will be stretched 5x its original to show the heavier mass exerted onto it. 2) The spring constant is the slope of the stretch and force of a spring 3) The weight in Newtons is equal to the mass in kg multiplied by gravity. 4) That number needs to be multiplied by gravity's force in order to find someone's weight using a bathroom scale.
Physics To Go 1A) w = mass(gravity) w = (100)(9.8) w = 980 kg 1B) w =mass(gravity) w = 10(9.8) w = 98 kg 1C) w = mass(gravity) w = 60(9.8) w = 588 2A) 130(4.4) = 572 N 2B) 1000(4.4) = 4400 N 2C) 50(4.4) = 2260 N 3) 3D) The slope is 6.7441, and that shows the spring constant.
4) F(s) = -kx 12 = -k(.03) 400 = -k k = -400 N/m
5) The force and the spring stretch are positively correlated; when one increases or decreases, so does the other. 6) The higher the spring force constant, the more force is needed to straighten it out. For example, a 15 N/cm spring is harder to stretch than a 10 N/cm spring.
7) F(s) = -kx 3 = -k(.02) 150 = -k k = -150 N/m
8) A spring scale compresses when a weight is pressed upon it, and the spring moves an arrow to show the weight. The tighter the compression, the heavier the weight.
What Do You Think Now? The calibration for the two very different objects varies too much to use the same scale. As for the spring force, the constant is proportional to the distance it stretches, and therefore moves the arrow to the designated number to determine one's weight.
Section 6
What Do You See?
The fat guy is pushing down on the scale while the air is pushing down on his box. The mouse is being pushed upward but is applying little force to its scale.
What Do You Think?
I do think your weight changes when you are on a roller coaster at certain spots. When I've ridden roller coasters in the past, I feel lighter at the top and then as I'm accelerating downward, much heavier.
Physics Talk Newton's first law: object at rests stays at rest, or in motion stays in motion, unless acted on by unbalanced force Newton's second law: unbalanced force creates an acceleration
The bigger force is in the same direction as acceleration
To do this draw motion map and free body diagram
increasing right
v ----> ----> t > f a
increasing left
v <---- <---- f > t a
Checking Up 1) a = f/m shows that when an object is moving at constant speed there is zero acceleration, so there are no net forces acting on it. 2 & 3) When the roller coaster accelerates upward, there is a net force acting on the object. This makes you feel heavier than you actually are, and the reading on the scale will verify this. Because there is a net force acting on you, it puts more force on the scale. 4) Because you are in free fall, you will feel less than you normally weigh. Because everything in the elevator is in free fall as well, there is no force connecting the scale to yourself, so the scale would read zero. 5) Air resistance slows down rain drops
Physics To Go 1A) vf = vi + at vf = 9.8(2) vf = 19.6 m/s
1B) vf = vi + at vf = 9.8(5) vf = 49 m/s
1C) vf = vi + at vf = 9.8(10) vf = 98 m/s
2A) vf = vi +at vf = 1.6(2) vf = 3.2 m/s
2B) vf = vi + at vf = 1.6(5) vf = 8 m/s
2C) vf = vi + at vf = 1.6(10) vf = 16 m/s
4)
Motion of the Elevator
Acceleration (up, down, zero)
Relative Scale Reading (greater, less or equal to weight)
At rest, bottom floor
zero
equal
Starting at Rest, Increasing Up
up
greater
Continuing to move, Constant Up
zero
equal
Slowing down to top floor, Decreasing Up
down
less
At rest, top floor
zero
equal
Starting at rest, Increasing Down
down
less
Continuing to move, Constant Down
zero
equal
Coming to a stop on the ground floor
up
greater
5) change in force = ma
6) It will appear heavier than the actual weight because the normal force is greater than weight.
7A) You will feel lighter than normal and the scale will read a lighter number. 7B) change in force = ma N - mg = ma N = ma + mg N = 50(-1.5) + 50(9.8) N = - 75 + 490 N = 415 N
8A) w = mg 50(9.8) = 490 N 8B) Net force = ma Net force = 50(2) 100 + 490 = 590 N 8C) N - w = ma N = w = 490 N
9) When there is no acceleration, there is normal weight. When there is acceleration pointing downwards, the net force points down and there is no apparent weight. When there's acceleration upward, the net force also points up and therefore there is a heavier apparent weight.
10) Our roller coaster targets extreme riders, and the thrills come from fast acceleration. Sharp turns, quick acceleration changes, and steep drops keep the rider excited.
What Do You Think Now?
No your actual weight does not change on a roller coaster, however, you may feel heavier or lighter at certain points. When you accelerate upward, you will feel heavier whereas accelerating downward makes you feel lighter.
Section 7
What Do You See?
The people look like they are falling off the track because the cart wants to continue moving tangent from the curve.
What Do You Think?
The cart is moving at such a fast speed that it can continue around the loop without causing people to fall out. There is centripetal force keeping the cart moving around the loop.
Physics Talk Normal force: the force acting perpendicular to the surface Centripetal force: any force directed toward the center that causes an object to follow a circular path at constant speed Centripetal acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed Uniform Circular Motion: tangential speed, usually constant
if Ac = 0, then moving in a straight like
Change in centripetal force = m(v^2) / r
v^2 / r = centripetal acceleration
Radius increases, Centripetal force decreases
Mass increases, Centripetal force increases
Velocity increases, Centripetal force decreases
Checking Up 1) Centripetal force. 2) Yes. 3) Weight and normal. 4) Normal. 5) The mass has a direct relationship, the radius has a indirect inverse, and the centripetal acceleration has a squared inverse.
Physics To Go 1) 2A) Friction 2B) The car will move tangent to the circle 6A) The velocity remains constant at 20 m/s 6B) Yes, the direction does. 6C) Change in velocity = v2 - v1 = v2 + (-v1) 20^2 + 20^2 = SQRT800 tan(pheta) = 20/20 pheta = 45 degrees 28.3 m/s at 45 degrees North West
7) Ac = v^2 / r = 20^2 / 200 Ac = 2 m/s
10) Fast
Required Centripetal Force
Force of Gravity (weight)
Normal Force
Top of loop
4,000 N
500 N
3,500 N
Bottom of loop
6,000 N
500 N
6,500 N
Slow
Required Centripetal Force
Force of Gravity (weight)
Normal Force
Top of loop
800 N
500 N
300 N
Bottom of loop
2,800 N
500 N
3,300 N
13A) They seem heavier 13B) It is impossible to tell if weight is greater than normal force, but inertia makes it feel heavier 13C) They appear heavier 13D) They seem heavier 13E) No change.
14A) Up 14B) Down 14C) Up 14D) Up 14E) No force 14F) Sideways 14G) Sideways
What Do You Think Now?
Due to centripetal acceleration, you feel heavier when you go around a loop, but the acceleration is directed towards the middle. This holds you in place, and because the acceleration is greater than gravity, you can never be in free fall.
Section 8
What Do You See? It looks like people are making a large effort to push a cart up the hill to reach maximum GPE
What Do You Think? Because GPE remains the same, the amount of energy is just transferred but never changed.
Physics Talk Work: the product of displacement and the force in the direction of the displacement; the energy transferred to an object Power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred Watt: the SI unit for power; 1 W = 1 J/s
Power is the rate of the energy dissipation (uses up)
How to stop a roller coaster
Compression of spring
Thermal energy
Checking Up
1) GPE is at the top 2) The work due to pulling up the cart is GPE at the top 3) The power lessens over time 4) It's converted to work or EPE 5) Watt
Physics To Go
1A) All of the energy at the top is GPE 1B) GPE / h 1C) All of it. GPE = EPE 1D) 1/2kx^2 1E) GPE 1F) When you just touch the spring you begin to slow down
2A) There is no acceleration. 2B) w = fd w = 60(0.5) w = 30 J 2C) w = fd w = 40(75) w = 3000 J 2D) w = fd w = 500(0.7) w = 350 J
3) Electrical energy is costly and streams directly to the object; it isn't the type of energy that is required to stay within a system.
4) It would have to be heavier so the energy could bring the cart to the top. In order to maximize GPE, more power would be needed to push the cart.
5A) w = GPE w = 10000(20) w = 200,000 J 5B) p = w / t p = 200,000 / 150 p = 1333.3 J
6) Work is needed to lift the cart to the top, where the energy is converted to GPE. On the way down, that energy is turned into KE. While the cart goes through a vertical loop, KE and GPE are transferred between each other. KE remains in play during the rest of the ride until EPE creates a break to stop the cart at the end of the ride.
What Do You Think Now?
The incline of a hill only changes the amount of power, but never the amount of work needed. It is only harder to walk up a steep incline because it involves utilizing more power.
Section 9
What Do You See? The girl is filling up her paper with equations to find the amount of energy. It's easily calculable, whereas the boy needs more information to determine the force needed for the roller coaster.
What Do You Think?
The parts where there are sharp turns and changes in accelerations make the ride the most fun and exciting.
Physics Talk
Checking Up 1) Pythagorean Theorem is needed to add vector quantities. 2) Energy is a scaler and force is a vector 3) We would need to know the GPE, KE, and the total energy. We can use them to find height and velocity. 4) No, the path does not change the amount of energy 5) Work is needed to change the amount of energy
Physics to Go
1) 2) The accelerations will be different although their velocities remain the same. This is due to a longer track accelerating slowly but building up speed, while the shorter track accelerates more quickly but only does it for so long. If the tracks start out at the same height and end in the same place, the kinetic energy and the velocity will be the same.
5) When given a height or velocity, it is always best to look for the x factor in terms of energy. When you are given specifics like a roller coaster at 20 meters in height that weighs 5 kg, you are able to find the velocity at the end of the track. The height is used for GPE whereas the KE is used to find the speed at the bottom of the track. In order to find net force, you need to draw a free body diagram and show where the forces are pointing at.
6-7A)
7B) The total energies are the same at both points because the total energy is the same in each particular system. The energy is just transferred from GPE to KE. 7C) The KE starts at the same height and therefore is the same. 7D) The height is the only other element is the only thing that determines GPE and then that number is transferred into KE.
What Do You Think Now?
When there are sharp turns from a small radius, the whipping feeling is much stronger than wider turns. The whipping showcases a greater acceleration and creates a more thrilling ride.
Section 10
What Do You See? There are hundreds of carts falling off tracks and into lakes, and people are flying out.
What Do You Think? The aspect of possible death is fascinating and definitely increases the risk of riding a roller coaster. The occurrence of this happening is so slim that you may be worried about it for a little bit but by the 3rd ride you completely disregard it. However, if 1 out of every 2 riders died, absolutely no one would ride roller coasters except those who are suicidal.
Physics Talk
Acceleration cannot exceed 4 Gs or 40 m/s.
Free fall = 1 G
Centripetal acceleration = v^2 / r
Centripetal force required in Newton's 2nd Law: f(net) = mv^2 / r
Checking Up
1) 4 Gs is the maximum acceleration. 2)
The velocity cannot exceed 40 m/s
The Gs need to be in between 1 & 4 Gs or else the cart would be in free fall.
3) At the bottom of the horizontal loop 4) At the bottom of the vertical loop
Physics To Go
1) The engineers need to make sure that the acceleration is under 4 Gs, and that the top of the loop must be bigger than 1 G to avoid free fall.
4C) KE = GPE(1) - GPE(2) KE = 50(9.8) - 20(9.8) KE = 294 J KE = 1/2(v^2) 294 = 1/2(v^2) v = 24 m/s
4D) ac = v^2 / r ac = 24^2 / 10 ac = 58 m/s^2
4E) The bottom of the loop exceeds the 4G cap and it's acceleration greatly surpasses it.
5A) ac = v^2 / r 9.8 = v^2 / 8 v = 8.9 m/s
5B) GPE = KE + GPE mgh = 1/2m(v^2) + mgh 9.8h = 1/2(8.9^2) + 9.8(16) h = 20.1
6) ac = v^2 / r ac = 12^2 / 18 ac = 8 m/s^2
6B) Fc = mv^2 / r Fc = 900(12^2) / 18 Fc = 7,200 N
6C) The friction from the wheels on the track
7A) ac = v^2 / r ac = 20^2 / 15 ac = 26.7 m/s^2
7B) Fc = m(v^2) / r Fc = 900(20^2) / 15 Fc = 24,000 N
7C) The roller coaster can use up to 25,000 N, and the coaster in 7B is 1,000 N under the maximum.
8A) No, mass is not a factor in centripetal acceleration (v^2 / r). 8B) The mass will be omitted because the speed does not change. 8C) The normal force will increase when the weight increases, and the track's strength needs to increase with the enlargement of the weight.
Physics Plus
What Do You Think Now?
The loops and hills are the most dangerous because if they don't have enough or too much Gs, the carts can be in free fall or simply fly off the track. Roller coaster engineers need to be aware to this pertinent information to keep riders safe.
Table of Contents
Initial Research
Possessed: the ride features zero-gravity and cobra rolls and corkscrews. A cobra roll takes the rider upside down twice, and a corkscrew resembles a typical loop that has been stretched out. In a corkscrew, riders are angled at 90 degrees horizontally from the incoming track.
Talon: the ride is floorless and uses a zero-gravity roll and an Immelman loop. The former places the center of gravity on the rider's heart to make him feel weightless, and the latter is an inverted loop where the rider's head is perpendicular to the track below him.
http://en.wikipedia.org/wiki/Immelmann_loop#Immelmann_loop
What Do You See?
Someone is being pushed in a wheely chair at various velocities and accelerations like they are on a roller coaster.
What Do You Think?
The parts that have the greatest amount of acceleration and turns creates the loudest screams, like the loops.
Physics Talk
Scaler: a quantity that has magnitude (size/amount), but no direction
Displacement: the difference in position between a final position; it depends only on the endpoints, not the path; displacement is a vector quality, it has magnitude (size) and direction
Vector: a quantity that has both magnitude (size/amount) and direction
Speed: distance traveled divided by the time elapsed; speed is a scaler quantity, it has no direction
Velocity: displacement divided by the time elapsed; velocity is a vector quantity, it has magnitude and direction
Acceleration: The change in velocity divided by the time elapsed; acceleration is a vector quantity, it has magnitude and direction
Checking Up
1) Displacement is the difference in position between a final position, whereas distance is the total difference between the start and the final positions.
2) 0 km because you wound up where you started
3) Speed is distance divided by time whereas velocity is displacement divided by time.
4) Total change in velocity over total change in distance = acceleration
What Do You Think Now?
The downward hills cause the most amount of acceleration, therefore producing the loudest scream. During the investigation, I felt the most jolted when experiencing quick accelerations.
Physics To Go
1)
2) The acceleration around curves and drops creates the largest thrills.
3A) La Paz in Bolivia has the greatest speed; it travels the greatest distance
3B) v = d/t
v = 40,000 / 24
v = 1666 2/3 m/s
3C) It has a high speed but because of its consistency it does not feel like you are going fast
4) a = vf - vi / t
a = 16 - 4 / 3
a = 4 m/s^2
5A) Speed
5B) Velocity
5C) Acceleration
5D) Distance
5E) Displacement
6) v = d/t
v = 0.1/2
v = .05 m/s
7) v = d/t
0.05 = .05/t
t = 1 s
8) a = v/t
a = vf - vi / t
a = 25-0 / 10
a = 2.5 m/s^2
10A) To make it more enjoyable for younger kids, I would alter the angle to make it less extreme for the kids. Anything to steep or scary would be too scary.
10B)
Section 2
What Do You See?
The people around the bend are sleeping, while the people going down the hill are screaming.
What Do You Think?
The steel roller coaster has the biggest thrill because of its steeper angle in comparison to the wooden roller coaster's 60 degree angle.
Physics Talk
GPE: The energy a body possesses as a result of its position in a gravitational field
KE: The energy an object possesses because of its speed
Joule: The unit for energy
Mechanical Energy: The sum of GPE + KE
Bar Chart:
Checking Up
1) When lengthening the incline, the ball will have a faster velocity at the bottom of the ramp.
2) Because GPE = mgh, any increase in a variable will increase the amount of energy in the object's potential energy.
3) The same goes for kinetic energy as it does for GPE. However, velocity is the only variable that is squared, so it carries more weight than the rest.
4) The cart starts with GPE and that turns into KE when it is released down the ramp. Because mechanical energy is GPE + KE, then the energy remains the same.
5) KE + GPE(bottom) = KE + GPE(top)
3/4(40,000)(Kinetic Energy) + 1/4(40,000)(GPE) = 0 + 40,000
KE = 30,000 J
What Do You Think Now?
When the carts start at the same height, their velocity and final magnitude are the same. Regardless of the incline, the carts will have the same velocity when traveling the same distance; however, the shorter track is going to be the one with the cart to finish first. This proves that the bigger the acceleration, the bigger the thrill.
Physics To Go
1) The speeds are both the same because the distance does not change. However, graph B would be faster if friction played a role.
3)
5)
8) KE and GPE both have mass in their equations, so when set equal to one another the masses cancel out; any system that uses gravity doesn't need mass to be solved.
9A) Point B showcases where the energy has changed from the highest GPE to the highest KE. The acceleration is maximized here, but as it goes back up the hill, the object will lose its KE but gain GPE proportionally.
9B) Ignoring friction, points B and G are the same height off of the ground and therefore have the same GPE and KE.
9C) Point D is where the object moves the fastest because of its low GPE and high KE.
Section 3
What Do You See?
Students are playing with spring toys and measuring its vertical distance.
What Do You Think?
Roller coaster carts usually need to go up a hill, so they either get pulled or move up a track. Carts full of people need more energy to lift it because the mass is now heavier.
Physics Talk
Spring Potential Energy: the energy stored in a spring due to its compression or stretch
Checking Up
1) That energy is then translated into kinetic energy once it is popped upward.
2) Energy cannot be created or destroyed, so the 2 J of SPE is transferred as 2 J of KE
3) Once again, energy cannot be created or destroyed. That energy is now 2 J of GPE
4) SPE = 1/2(k)(x^2)
Physics To Go
5) The cart moves up a hill and at its peak it has a maximum GPE. Once that energy is transformed into KE, it then can move up and down hills. However, the maximum energy has been reached, so the next hill cannot exceed the previous.
6) The cart has a certain amount of kinetic energy at the start of the roller coaster. To go up and down hills, the cart needs to maintain a certain energy to do so; when the cart does not have the amount, it slows down until it finally will come to a stop.
7) GPE = mgh
= 300(9.8)(15)
= 44,100 J
8A) KE = 1/2m(v^2)
= 1/2(400)(15^2)
= 45,000 J
8B) The GPE will be 45,000 J of energy if the kinetic energy is 0
8C) 45000 = 400(9.8)h
h = 11.48 m
9) The GPE is maximized at its highest point, so when rising it's GPE is increasing and when it falls its decreasing.
10) All three people will have the same GPE in the end, but whoever walks on route A will gain the most GPE the fastest.
11A) GPE = KE
0.02(9.8)(0.4) = 1/2(0.02)(2.7^2)
0.0784 = 0.0729
The values are very similar.
11B) mgh + 1/2m(v^2) = SPE
0.02(9.8)(0.4) + 1/2(0.02)(2.7^2) = SPE
0.0784 + 0.0729 = SPE
11C) The height would reach 1/3 of its original height.
12A) GPE = EPE
mgh = 1/2k(x^2)
300(9.8)(18) = 1/2(4)(x^2)
52920 = 2x^2
26460 = x^2
x = 162.67 m
12B) GPE = EPE
mgh = 1/2k(x^2)
400(9.8)(18) = 1/2(4)(x^2)
70560 = 2x^2
35280 = x^2
x = 187.83 m
13) EPE = KE
1/2k(x^2) = KE
1/2(40)(.3^2) = KE
KE = 1.8 J
What Do Yu Think Now?
With most roller coasters, a chain drags the carts up a hill to reach a certain height in order to fulfill the needed amount of energy to ride the track. The amount of energy needed to lift the cart fully depends on the mass of the cart with the maximum weight of all of the passengers. This is why roller coasters have weight limits, to ensure safety when reaching maximum GPE.
Section 4
What Do You See?
The astronauts on the moon are on a roller coaster, but do not seem to be having fun. However, Jupiter's roller coaster has them screaming in delight.
What Do You Think?
Gravity points to the center of the Earth, regardless of what direction you are facing. Liquids that drain in Australia turn the opposite way than in America due to the change in gravity.
Physics Talk
Gravitational Field: the gravitational influence in the space around a massive object
Inverse-square Relationship: the relationship between the magnitude of a gravitational force and the distance from the mass. This also describes how electrostatic forces depend on the distance from an electrical charge
Newton's Law of Universal Gravitation: all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bodies increases.
Gravity: the force of attraction between the two bodies due to their masses
Checking Up
1) Gravity pulls towards the center of the earth.
2) Gravity is stronger where the lines are closest together whereas the further away from the center, the weaker the gravity.
3) The gravity is then cubed.
4) The moon and its orbit is held together by the same gravity
5) The shape of the orbit around the sun is elliptical.
Physics Plus
1) a = (v^2)(r)
2) v = d/t
(2pi)(3.84 x 10^8) / 2440800
v = 998.51 m/s
3) a = v^2 / r
a = 998.51^2 / (3.84 x 10^8)
a = 0.0025 m/s^2
Physics To Go
1) 1/25
2A) 1/4 of the force
2B) 1/9 of the force
2C) 1/16 force.
3) Every mass has gravitational force, so the GPE will always be present. This is a secure fact, so there is no reason to distrust it.
4) Both values of GPE and KE (when set equal to one another) are very similar. The only slight difference is that the point at the top will have a miniscule amount less than the cart at the bottom because of the difference in height. The closer to the earth, the more gravity it will have.
5A) The water sits on the Earth.
5B&C) More water on the side facing the moon because the water is attracted to the moon's pull
6A&B) Water's polarity has a gravitational pull, and the fish also has GPE. This keeps the water and the fish grounded.
7A) 1/4 of the force.
7B) 1/9 of the force.
7C) 1/16 of the force.
7D) 4x the force
8A) Doubles
8B) Triples
8C) Quadruples
8D) Half
9A) Quadruples
9B) 9x the force
9C) 16x the force
9D) 1/4 of the force
10A) Doubles
10B) 9x the force
10C) 6x the force
What Do You Think Now?
Attraction between two masses accounts for gravity's direction. Because everything is pulled towards the center of the Earth, people do not feel upside down regardless of their geographical location. Gravity acts on all masses, so the ground is attracted to the center of the earth, and we are attracted to the ground.
Section 5
What Do You See?
The same piece of meat is being weighed by 2 different scales - one at a deli and one at a lab.What Do You Think?
A scale that measures an elephant would not be able to make sense of the small mass of the canary and vice versa. A scale works by a mass stepping on it and stretching the coil. The distance is measured and recorded for the person to see their weight, also in combination with gravity.Physics Talk
Hooke's Law: Fs = -kx
(F = force of spring in N; k = spring constant in N/m; x = stretch distance in m)
Checking Up
1) The spring will be stretched 5x its original to show the heavier mass exerted onto it.
2) The spring constant is the slope of the stretch and force of a spring
3) The weight in Newtons is equal to the mass in kg multiplied by gravity.
4) That number needs to be multiplied by gravity's force in order to find someone's weight using a bathroom scale.
Physics To Go
1A) w = mass(gravity)
w = (100)(9.8)
w = 980 kg
1B) w =mass(gravity)
w = 10(9.8)
w = 98 kg
1C) w = mass(gravity)
w = 60(9.8)
w = 588
2A) 130(4.4) = 572 N
2B) 1000(4.4) = 4400 N
2C) 50(4.4) = 2260 N
3)
3D) The slope is 6.7441, and that shows the spring constant.
4) F(s) = -kx
12 = -k(.03)
400 = -k
k = -400 N/m
5) The force and the spring stretch are positively correlated; when one increases or decreases, so does the other.
6) The higher the spring force constant, the more force is needed to straighten it out. For example, a 15 N/cm spring is harder to stretch than a 10 N/cm spring.
7) F(s) = -kx
3 = -k(.02)
150 = -k
k = -150 N/m
8) A spring scale compresses when a weight is pressed upon it, and the spring moves an arrow to show the weight. The tighter the compression, the heavier the weight.
What Do You Think Now?
The calibration for the two very different objects varies too much to use the same scale. As for the spring force, the constant is proportional to the distance it stretches, and therefore moves the arrow to the designated number to determine one's weight.
Section 6
What Do You See?
The fat guy is pushing down on the scale while the air is pushing down on his box. The mouse is being pushed upward but is applying little force to its scale.What Do You Think?
I do think your weight changes when you are on a roller coaster at certain spots. When I've ridden roller coasters in the past, I feel lighter at the top and then as I'm accelerating downward, much heavier.Physics Talk
Newton's first law: object at rests stays at rest, or in motion stays in motion, unless acted on by unbalanced force
Newton's second law: unbalanced force creates an acceleration
- The bigger force is in the same direction as acceleration
- To do this draw motion map and free body diagram
- increasing right
v---->
----> t > f
a
- increasing left
v<----
<---- f > t
a
Checking Up
1) a = f/m shows that when an object is moving at constant speed there is zero acceleration, so there are no net forces acting on it.
2 & 3) When the roller coaster accelerates upward, there is a net force acting on the object. This makes you feel heavier than you actually are, and the reading on the scale will verify this. Because there is a net force acting on you, it puts more force on the scale.
4) Because you are in free fall, you will feel less than you normally weigh. Because everything in the elevator is in free fall as well, there is no force connecting the scale to yourself, so the scale would read zero.
5) Air resistance slows down rain drops
Physics To Go
1A) vf = vi + at
vf = 9.8(2)
vf = 19.6 m/s
1B) vf = vi + at
vf = 9.8(5)
vf = 49 m/s
1C) vf = vi + at
vf = 9.8(10)
vf = 98 m/s
2A) vf = vi +at
vf = 1.6(2)
vf = 3.2 m/s
2B) vf = vi + at
vf = 1.6(5)
vf = 8 m/s
2C) vf = vi + at
vf = 1.6(10)
vf = 16 m/s
4)
5) change in force = ma
6) It will appear heavier than the actual weight because the normal force is greater than weight.
7A) You will feel lighter than normal and the scale will read a lighter number.
7B) change in force = ma
N - mg = ma
N = ma + mg
N = 50(-1.5) + 50(9.8)
N = - 75 + 490
N = 415 N
8A) w = mg
50(9.8) = 490 N
8B) Net force = ma
Net force = 50(2)
100 + 490 = 590 N
8C) N - w = ma
N = w = 490 N
9) When there is no acceleration, there is normal weight. When there is acceleration pointing downwards, the net force points down and there is no apparent weight. When there's acceleration upward, the net force also points up and therefore there is a heavier apparent weight.
10) Our roller coaster targets extreme riders, and the thrills come from fast acceleration. Sharp turns, quick acceleration changes, and steep drops keep the rider excited.
What Do You Think Now?
No your actual weight does not change on a roller coaster, however, you may feel heavier or lighter at certain points. When you accelerate upward, you will feel heavier whereas accelerating downward makes you feel lighter.Section 7
What Do You See?
The people look like they are falling off the track because the cart wants to continue moving tangent from the curve.What Do You Think?
The cart is moving at such a fast speed that it can continue around the loop without causing people to fall out. There is centripetal force keeping the cart moving around the loop.Physics Talk
Normal force: the force acting perpendicular to the surface
Centripetal force: any force directed toward the center that causes an object to follow a circular path at constant speed
Centripetal acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed
Uniform Circular Motion: tangential speed, usually constant
Checking Up
1) Centripetal force.
2) Yes.
3) Weight and normal.
4) Normal.
5) The mass has a direct relationship, the radius has a indirect inverse, and the centripetal acceleration has a squared inverse.
Physics To Go
1)
2A) Friction
2B) The car will move tangent to the circle
6A) The velocity remains constant at 20 m/s
6B) Yes, the direction does.
6C) Change in velocity = v2 - v1
= v2 + (-v1)
20^2 + 20^2 = SQRT800
tan(pheta) = 20/20
pheta = 45 degrees
28.3 m/s at 45 degrees North West
7) Ac = v^2 / r
= 20^2 / 200
Ac = 2 m/s
10)
Fast
13B) It is impossible to tell if weight is greater than normal force, but inertia makes it feel heavier
13C) They appear heavier
13D) They seem heavier
13E) No change.
14A) Up
14B) Down
14C) Up
14D) Up
14E) No force
14F) Sideways
14G) Sideways
What Do You Think Now?
Due to centripetal acceleration, you feel heavier when you go around a loop, but the acceleration is directed towards the middle. This holds you in place, and because the acceleration is greater than gravity, you can never be in free fall.
Section 8
What Do You See?It looks like people are making a large effort to push a cart up the hill to reach maximum GPE
What Do You Think?
Because GPE remains the same, the amount of energy is just transferred but never changed.
Physics Talk
Work: the product of displacement and the force in the direction of the displacement; the energy transferred to an object
Power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred
Watt: the SI unit for power; 1 W = 1 J/s
Checking Up
1) GPE is at the top2) The work due to pulling up the cart is GPE at the top
3) The power lessens over time
4) It's converted to work or EPE
5) Watt
Physics To Go
1A) All of the energy at the top is GPE1B) GPE / h
1C) All of it. GPE = EPE
1D) 1/2kx^2
1E) GPE
1F) When you just touch the spring you begin to slow down
2A) There is no acceleration.
2B) w = fd
w = 60(0.5)
w = 30 J
2C) w = fd
w = 40(75)
w = 3000 J
2D) w = fd
w = 500(0.7)
w = 350 J
3) Electrical energy is costly and streams directly to the object; it isn't the type of energy that is required to stay within a system.
4) It would have to be heavier so the energy could bring the cart to the top. In order to maximize GPE, more power would be needed to push the cart.
5A) w = GPE
w = 10000(20)
w = 200,000 J
5B) p = w / t
p = 200,000 / 150
p = 1333.3 J
6) Work is needed to lift the cart to the top, where the energy is converted to GPE. On the way down, that energy is turned into KE. While the cart goes through a vertical loop, KE and GPE are transferred between each other. KE remains in play during the rest of the ride until EPE creates a break to stop the cart at the end of the ride.
What Do You Think Now?
The incline of a hill only changes the amount of power, but never the amount of work needed. It is only harder to walk up a steep incline because it involves utilizing more power.Section 9
What Do You See?
The girl is filling up her paper with equations to find the amount of energy. It's easily calculable, whereas the boy needs more information to determine the force needed for the roller coaster.
What Do You Think?
The parts where there are sharp turns and changes in accelerations make the ride the most fun and exciting.Physics Talk
Checking Up
1) Pythagorean Theorem is needed to add vector quantities.
2) Energy is a scaler and force is a vector
3) We would need to know the GPE, KE, and the total energy. We can use them to find height and velocity.
4) No, the path does not change the amount of energy
5) Work is needed to change the amount of energy
Physics to Go
1)2) The accelerations will be different although their velocities remain the same. This is due to a longer track accelerating slowly but building up speed, while the shorter track accelerates more quickly but only does it for so long. If the tracks start out at the same height and end in the same place, the kinetic energy and the velocity will be the same.
3A) Distance - Scaler
3B) Displacement - Vector
3C) Speed - Scaler
3D) Velocity - Vector
3E) Acceleration - Vector
3F) Force - Vector
3G) KE - Scaler
3H) PR - Scaler
3I) Work - Vector
4A) Scaler
4B) Vector
4C) Scaler
4D) Vector
5) When given a height or velocity, it is always best to look for the x factor in terms of energy. When you are given specifics like a roller coaster at 20 meters in height that weighs 5 kg, you are able to find the velocity at the end of the track. The height is used for GPE whereas the KE is used to find the speed at the bottom of the track. In order to find net force, you need to draw a free body diagram and show where the forces are pointing at.
6-7A)
7B) The total energies are the same at both points because the total energy is the same in each particular system. The energy is just transferred from GPE to KE.
7C) The KE starts at the same height and therefore is the same.
7D) The height is the only other element is the only thing that determines GPE and then that number is transferred into KE.
What Do You Think Now?
When there are sharp turns from a small radius, the whipping feeling is much stronger than wider turns. The whipping showcases a greater acceleration and creates a more thrilling ride.Section 10
What Do You See?
There are hundreds of carts falling off tracks and into lakes, and people are flying out.
What Do You Think?
The aspect of possible death is fascinating and definitely increases the risk of riding a roller coaster. The occurrence of this happening is so slim that you may be worried about it for a little bit but by the 3rd ride you completely disregard it. However, if 1 out of every 2 riders died, absolutely no one would ride roller coasters except those who are suicidal.
Physics Talk
Checking Up
1) 4 Gs is the maximum acceleration.2)
3) At the bottom of the horizontal loop
4) At the bottom of the vertical loop
Physics To Go
1) The engineers need to make sure that the acceleration is under 4 Gs, and that the top of the loop must be bigger than 1 G to avoid free fall.2A) mgh + 1/2m(v^2) = mgh
(9.8)h + 1/2(20^2) = (9.8)h
20 = h
2B) a(c) = v^2 / r
a(c) = (20^2) / 12
a(c) = 33 m/s^2
2C) Yes it is 3.4 Gs
2D) a(c) = = v^2 / r
39.6 = v^2 / 12
v = 22 m/s
2E) a(c) = v^2 / r
39.6 = v^2 / r
v = 17 m/s
3A) a(c) = v^2 / r
a(c) = 25^2 / 10
a(c) = 63 m/s^2
3B) No, it's 6.3 Gs
4A) mgh = 1/2m(v^2)
9.8(50) = 0.5(v^2)
v = 31 m/s
4B) a(c) = v^2 / r
a(c) = 31^2 / 10
a(c) = 96 m/s^2
4C) KE = GPE(1) - GPE(2)
KE = 50(9.8) - 20(9.8)
KE = 294 J
KE = 1/2(v^2)
294 = 1/2(v^2)
v = 24 m/s
4D) ac = v^2 / r
ac = 24^2 / 10
ac = 58 m/s^2
4E) The bottom of the loop exceeds the 4G cap and it's acceleration greatly surpasses it.
5A) ac = v^2 / r
9.8 = v^2 / 8
v = 8.9 m/s
5B) GPE = KE + GPE
mgh = 1/2m(v^2) + mgh
9.8h = 1/2(8.9^2) + 9.8(16)
h = 20.1
6) ac = v^2 / r
ac = 12^2 / 18
ac = 8 m/s^2
6B) Fc = mv^2 / r
Fc = 900(12^2) / 18
Fc = 7,200 N
6C) The friction from the wheels on the track
7A) ac = v^2 / r
ac = 20^2 / 15
ac = 26.7 m/s^2
7B) Fc = m(v^2) / r
Fc = 900(20^2) / 15
Fc = 24,000 N
7C) The roller coaster can use up to 25,000 N, and the coaster in 7B is 1,000 N under the maximum.
8A) No, mass is not a factor in centripetal acceleration (v^2 / r).
8B) The mass will be omitted because the speed does not change.
8C) The normal force will increase when the weight increases, and the track's strength needs to increase with the enlargement of the weight.
Physics Plus
What Do You Think Now?
The loops and hills are the most dangerous because if they don't have enough or too much Gs, the carts can be in free fall or simply fly off the track. Roller coaster engineers need to be aware to this pertinent information to keep riders safe.